30,520 research outputs found
Inherited Twistor-Space Structure of Gravity Loop Amplitudes
At tree-level, gravity amplitudes are obtainable directly from gauge theory
amplitudes via the Kawai, Lewellen and Tye closed-open string relations. We
explain how the unitarity method allows us to use these relations to obtain
coefficients of box integrals appearing in one-loop N=8 supergravity amplitudes
from the recent computation of the coefficients for N=4 super-Yang-Mills
non-maximally-helicity-violating amplitudes. We argue from factorisation that
these box coefficients determine the one-loop N=8 supergravity amplitudes,
although this remains to be proven. We also show that twistor-space properties
of the N=8 supergravity amplitudes are inherited from the corresponding
properties of N=4 super-Yang-Mills theory. We give a number of examples
illustrating these ideas.Comment: 32 pages, minor typos correcte
Symbols of One-Loop Integrals From Mixed Tate Motives
We use a result on mixed Tate motives due to Goncharov
(arXiv:alg-geom/9601021) to show that the symbol of an arbitrary one-loop
2m-gon integral in 2m dimensions may be read off directly from its Feynman
parameterization. The algorithm proceeds via recursion in m seeded by the
well-known box integrals in four dimensions. As a simple application of this
method we write down the symbol of a three-mass hexagon integral in six
dimensions.Comment: 13 pages, v2: minor typos correcte
Grigori Kuzmin and Stellar Dynamics
Grigori Kuzmin was a very gifted dynamicist and one of the towering figures
in the distinguished history of the Tartu Observatory. He obtained a number of
important results in relative isolation which were later rediscovered in the
West. This work laid the foundation for further advances in the theory of
stellar systems in dynamical equilibrium, thereby substantially increasing our
understanding of galaxy dynamics.Comment: 10 pages, 1 figure, to appear in Baltic Astronomy, proceedings of the
conference "Expanding the Universe" held in Tartu, Estonia, 27-29 April, 201
The Five-Loop Four-Point Amplitude of N=4 super-Yang-Mills Theory
Using the method of maximal cuts, we construct the complete D-dimensional
integrand of the five-loop four-point amplitude of N = 4 super-Yang-Mills
theory, including nonplanar contributions. In the critical dimension where this
amplitude becomes ultraviolet divergent, we present a compact explicit
expression for the nonvanishing ultraviolet divergence in terms of three vacuum
integrals. This construction provides a crucial step towards obtaining the
corresponding amplitude of N = 8 supergravity useful for resolving the general
ultraviolet behavior of supergravity theories.Comment: 5 pages, 4 figures, RevTex. Ancillary file included. v2 minor
corrections, corrected references and overall phase in eq. (5), matching
journal versio
Mellin Amplitudes for Dual Conformal Integrals
Motivated by recent work on the utility of Mellin space for representing
conformal correlators in /CFT, we study its suitability for representing
dual conformal integrals of the type which appear in perturbative scattering
amplitudes in super-Yang-Mills theory. We discuss Feynman-like rules for
writing Mellin amplitudes for a large class of integrals in any dimension, and
find explicit representations for several familiar toy integrals. However we
show that the power of Mellin space is that it provides simple representations
even for fully massive integrals, which except for the single case of the
4-mass box have not yet been computed by any available technology. Mellin space
is also useful for exhibiting differential relations between various multi-loop
integrals, and we show that certain higher-loop integrals may be written as
integral operators acting on the fully massive scalar -gon in
dimensions, whose Mellin amplitude is exactly 1. Our chief example is a very
simple formula expressing the 6-mass double box as a single integral of the
6-mass scalar hexagon in 6 dimensions.Comment: 29+7 page
Feynman integrals via hyperlogarithms
This talk summarizes recent developments in the evaluation of Feynman
integrals using hyperlogarithms. We discuss extensions of the original method,
new results that were obtained with this approach and point out current
problems and future directions.Comment: 8 pages, 5 figures, Proceedings of "Loops & Legs 2014", Weimar
(Germany), April 27 -- May
On the Singularity Structure of Maximally Supersymmetric Scattering Amplitudes
We present evidence that loop amplitudes in maximally supersymmetric
Yang-Mills (SYM) beyond the planar limit share some of the
remarkable structures of the planar theory. In particular, we show that through
two loops, the four-particle amplitude in full SYM has only
logarithmic singularities and is free of any poles at infinity---properties
closely related to uniform transcendentality and the UV-finiteness of the
theory. We also briefly comment on implications for maximal ()
supergravity.Comment: 4 pages, 3 figure
Power Counting Regime of Chiral Effective Field Theory and Beyond
Chiral effective field theory complements numerical simulations of quantum
chromodynamics (QCD) on a space-time lattice. It provides a model-independent
formalism for connecting lattice simulation results at finite volume and a
variety of quark masses to the physical world. The asymptotic nature of the
chiral expansion places the focus on the first few terms of the expansion.
Thus, knowledge of the power-counting regime (PCR) of chiral effective field
theory, where higher-order terms of the expansion may be regarded as
negligible, is as important as knowledge of the expansion itself. Through the
consideration of a variety of renormalization schemes and associated
parameters, techniques to identify the PCR where results are independent of the
renormalization scheme are established. The nucleon mass is considered as a
benchmark for illustrating this general approach. Because the PCR is small, the
numerical simulation results are also examined to search for the possible
presence of an intrinsic scale which may be used in a nonperturbative manner to
describe lattice simulation results outside of the PCR. Positive results that
improve on the current optimistic application of chiral perturbation theory
beyond the PCR are reported.Comment: 18 pages, 55 figure
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